... since Tolkien in fact does not tell us any of the history that might account for the origins of the Shire's dual government, I am going to talk about the sources for the idea of such a system in Tolkien's own intellectual background.
One of these two sources, I believe, was two writers of the generation before Tolkien: G.K. Chesterton and Hilaire Belloc. Tolkien refers explicitly to Chesterton, notably in his essay "On Fairy Stories," and though I do not know of any such mention of Belloc, he does turn up elsewhere in the Inklings' writings — Lewis mentions his theory of Distributivism in That Hideous Strength (Lewis, 1946, p.19) — and it seems virtually certain that Tolkien had at least heard about it frequently.
Belloc and Chesterton were the two leading Catholic intellectuals in their generation in England; their prose and poetry was widely read; and they joined in advocating a social order which was in effect an idealization of the Middle Ages, a system in which as many people was possible were small property owners — most notably in Belloc's own The Servile State (Belloc, 1913 / 1977), but in many other writings as well.
John P. McCarthy's Hilaire Belloc: Edwardian Radical (McCarthy, 1978) traces the evolution of Belloc's views in detail, showing in his early views a synthesis of republican liberalism and Catholic traditionalism that Tolkien's own offhand remarks bear considerable resemblance to. The "estates, farms, workshops, and small trades" (Tolkien, 1965, p. 30) [Fellowship] that Tolkien describes could be a portrait of the society Belloc recommends. On the other side, Belloc's critique of modern industrialism as leading inevitably toward a revival of slavery seems akin in turn to Tolkien's fictional portrayal of Sauron and Saruman and to his factual comments about the horrors of the modern society.